John Walko Courtesy of EE Times Europe (11/26/2008 7:31 AM EST)

LONDON — Researchers at St Andrew's University in Scotland and Masaryk University in the Czech Republic have come up with a new way of using mathematics to describe an invisibility cloak.

Writing in this month's edition of New Journal of Physics, which focuses on Cloaking and Transformation Optics, Ulf Leonhardt of St Andrew's University and Toms Tyc of Masaryk University in the Czech Republic suggest their work could lead to a breakthrough in the development of broadband invisibility cloaks.

Tyc and Leonhardt use ideas from transformation optics to transmute the infinity mark on the refractive index into something more practical. Basically, the scientists have developed a recipe of materials to create optical illusions " some can be used for invisibility devices, others to make things perfectly visible.

"Our method works for optical singularities which are the curse of physics, often seeming intractable, but we have found a way of transmuting optical singularities with just harmless crystal defects as a side-effect," write Tyc and Leonhardt.

They suggest applications will probably first appear in wireless technology and radar, for electromagnetic microwaves instead of light, because the required materials for electromagnetic microwaves are easier to manufacture.

Researchers first began to move invisibility from the realm of Harry Potter to something approaching reality two years ago. British physicist John Pendry, working with American colleagues David Smith and David Schurig at Duke University, developed a "cloak" that could hide an object from a microwave beam. Microwaves, which range from one millimeter to one meter long, are much longer than visible light waves, which range from about 400 to 700 nanometers.

Smith and Schurig built the cloak with a type of laboratory-made material called a metamaterial, in their case made of copper wires patterned onto sheets of fiberglass. Metamaterials take advantage of the fact that all materials refract, or bend, light -- for example, water bends light so that underwater objects appear closer than they really are.

The metamaterial that Smith and Schurig built bent the microwaves in such a way that it guided them around the object, like water flowing around a rock in a stream.

Earlier this year, scientists at the University of California, Berkeley announced that they had developed a metamaterial that could negatively refract visible wavelengths of light -- a necessary step toward building a visible-light cloaking device.

Leonhardt and Tyc made their theoretical breakthrough by using non-Euclidean geometry to describe the workings of their cloak. Unlike the more familiar Euclidean geometry, non-Euclidean geometry is not restricted to describing space in terms of perpendicular axes.

In their work, the physicists used a non-Euclidean geometry based on the surface of a sphere, which they intersected with a Euclidean plane in an arrangement that resembles a globe partially wrapped by a piece of paper.

While the physicists have not actually built such a cloak, they say that there non-Euclidean approach could provide a blueprint for building a broadband cloak. In particular, it could be used to define the index of refraction at a specific point in the cloak — and for light travelling in a specific direction. This quantity is given by the ratio by which the transformation stretches space at that point to create the cloaked region.

The paper from Leonhardt and Tyc is available here

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